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Calculus/Implicit and ln differentiation

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Question
How would you solve this:

3y-x^(2)+ln(xy) = 2

Answer
I am assuming you are asked to find dy/dx.

Firstly, I will do a little manipulation of the LHS:

3y-x^(2)+ln(xy) = 2
3y-x^(2)+ln x + lny = 2

Differentiating this on both sides wrt x gives

         3 (dy/dx) -2x + 1/x +(1/y) (dy/dx) =0

         ( 3+ 1/y) (dy/dx) =2x -1/x

         (3y + 1)/y * (dy/dx) = (2x^2 - 1) /x
         
         dy/dx =  [(2x^2 - 1)*y] /[ x * (3y+1)]   (shown)

Hope this helps. Peace.  

Calculus

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Frederick Koh

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I can answer questions concerning calculus, complex numbers, vectors, statistics , algebra and trigonometry for the O level, A level and 1st/2nd year college math/engineering student.

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More than 7 years of experience helping out in various homework forums. Latest Presence is over at http://www.thestudentroom.co.uk/ . You can also visit my main maths website http://www.whitegroupmaths.com where I have designed "question locker" vaults to store tons of fully worked math problems. A second one is currently being built. Peace.

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